From a point on the ground, the angle of elevation of the bottom and top of a transmission tower fixed at the top of 30 m high building are $30°$ and $60°$, respectively. Find the height of the transm

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From a point on the ground, the angle of elevation of the bottom and top of a transmission tower fixed at the top of 30 m high building are $30°$ and $60°$, respectively. Find the height of the transmission tower. (Use $\sqrt{3} = 1.73$)

Accepted Answer

Step 1: Building AB of height 30m with transmission tower BP on top, angles 30° and 60° from point C on ground
Step 2: Height of building $AB = 30$ m. $BP$ = transmission tower $= h$ m. $\angle ACB = 30°$, $\angle ACP = 60°$. In $	riangle ABC$: $	an 30° = \frac{AB}{AC} \Rightarrow \frac{1}{\sqrt{3}} = \frac{30}{AC} \Rightarrow AC = 30\sqrt{3}$
Step 3: In $	riangle APC$: $	an 60° = \frac{AP}{AC} \Rightarrow \sqrt{3} = \frac{30 + h}{30\sqrt{3}} \Rightarrow 30\sqrt{3} 	imes \sqrt{3} = 30 + h$
Step 4: $\Rightarrow h = 90 - 30 = 60$. $	herefore$ Height of transmission tower $= 60$ m

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